Finite Group DatabasebetaFinite Group Databasebeta| order | 8766 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #17983938⋊C2 |
| derived, Sylow | C487 ⋊ C2×C9 |
| Hall | #17983938 ⋊ C2 |
| Hall | D487 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | D487⋊C3 |
| commutator, hypocenter | C487 | C2×C9 |
| Fitting, socle | C3×C487 | C2×C3 |
| LCS | G ▷ C487 | |
| UCS | C1 ◁ C3 | |
12 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,487,3|b^3=d,c^a=c^486,c^b=c^232261 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#17983938⋊C2 |
| maximal normal subgroup of | C2×#17983938⋊C2 |
| maximal quotient of | #17983938⋊C4, C2×#17983938⋊C2 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8766, 2);